Problem: Complete the equation of the line through $(4,-8)$ and $(8,5)$. Use exact numbers. $y=$
Let's find the slope: $\begin{aligned} \text{Slope}&=\dfrac{5-(-8)}{8-4} \\\\ &=\dfrac{13}{4} \end{aligned}$ The equation is $y=\dfrac{13}{4}x+b$ for some $b$. Let's plug the point $({8},{5})$ to find $b$ : $\begin{aligned} y&=\dfrac{13}{4} x+b \\\\ {5}&=\dfrac{13}{4}({8})+b \\\\ 5&=26+b \\\\ -21&=b \end{aligned}$ The equation is $y=\dfrac{13}{4}x -21$.